I once heard someone mention something to the tunee of the more connecting flights you make, the more upgrades you get, or the sooner you can earn a free trip or get upgrades. I looked on a couple of airlines websites, and didn't find any information about this. The only airline that would seem to make sense for would be Southwest. Does anyone know about this, or exactly how it works?

As you can see, the more you connect, the more you rack up your segment. In theory, if you connect through a hub, you'll achieve your elite status in half the time as opposed to flying non-stops, should you try to earn your elite status the segment wise. Most airlines will give you a minimum of 500 miles or the actual mileage flown- which ever one is greater. TWA used to give 750 miles minimum- which is quite generous. Of course, it doesn't matter how you earn your status- but if you're flying a lot of commuter flights, it'll most likely be the number of segments that saves the day. If you fly x-country flights often, it'll be your miles that will probably earn you that card.
Most airlines gives away promotional miles for new routes, opening of FF account and so on, but some of those miles don't count towards your elite status.
If you don't mind adding extra hour or so to your flight time, connecting is a great way to build FF points. But you're also exposing yourself for some nasty delays at hub airports.
But don't get too caught up in trying to collect FF miles. I know too many people who pay extra or travel at inconvenient times just to earn their status or to get a shot at an upgrade.